Anisotropic parametric plate discrete elements

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Abstract
A limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry. Typically, the plan form of these elements is a straight‐sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher‐order polynomials to approximate the deformed geometry. This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials. This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis. Consideration is given to automating the generation of these patches. Solutions are presented for several plate bending and plate stretching problems. The solutions are in good agreement with closed‐form solutions and photoelastic results in the case of a stress‐concentration problem. These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries.

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